Out of budget but the Goretex shake dry material is amazing, truly waterproof and breathable. Rapha do an insulated version but my preference would just be to layer underneath and get a shell. Then you’ve got the most flexible option. I’ve the 7Mesh version and it’s an amazing piece of kit.
Within budget I’d probably get a Gabba. They are good down to 6-8 degrees, anything colder than that and you need something warmer. They aren’t waterproof but pretty water resistant, they will let moisture through after a while. I’ve done a day in the alps in the rain in a Gabba and it was perfect for that, stayed dry-ish and breathable.
Rapha hardshell on the second hand market might be another option. I’ve got one from years back, semi-breathable but nicely waterproof and indestructible.